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On the homeomorphisms of a non-orientable surface

Published online by Cambridge University Press:  24 October 2008

W. B. R. Lickorish
W. B. R. Lickorish
Affiliation:
Pembroke College, Cambridge
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Extract

The purpose of this note is to answer a question asked in an earlier paper ((2), page 315). Let X be a closed, connected, non-orientable 2-manifold and f: X → X a homeomorphism. It was shown in (2) that f is isotopic to a product of homeomorphisms of two basic types, the c-homeomorphism, which will now be called a twist, and the Y-homeomorphism (see (2) for definitions). It was also proved that f cannot, in general, be expressed as a product of twists alone. The following result is proved here:

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 1 , January 1965 , pp. 61 - 64
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

REFERENCES

(1)Lickorish, W. B. R.A representation of orientable combinatorial three manifolds. Ann. of Math. (2) 76 (1962), 531–540.CrossRefGoogle Scholar
(2)Lickorish, W. B. R.Homeomorphisms of non-orientable two-manifolds. Proc. Cambridge Philos. Soc. 59 (1963), 307–317.CrossRefGoogle Scholar